Invariant Fields of Finite Irreducible Re ection Groups
نویسندگان
چکیده
We prove the following result: If G is a nite irreducible reeection group deened over a base eld k, then the invariant eld of G is purely transcendental over k, even if jGj is divisible by the characteristic of k. It is well known that in the above situation the invariant ring is in general not a polynomial ring. So the question whether at least the invariant eld is purely transcendental (Noether's problem) is quite natural.
منابع مشابه
Towards Spetses I
We present a formalization using data uniquely de ned at the level of the Weyl group of the construction and combinatorial properties of unipotent character shea ves and unipotent characters for reductive algebraic groups over an algebraic closure of a nite eld This formalization extends to the case where the Weyl group is re placed by a complex re ection group and in many cases we get families...
متن کاملFinite p-groups with few non-linear irreducible character kernels
Abstract. In this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.
متن کاملSome connections between powers of conjugacy classes and degrees of irreducible characters in solvable groups
Let $G$ be a finite group. We say that the derived covering number of $G$ is finite if and only if there exists a positive integer $n$ such that $C^n=G'$ for all non-central conjugacy classes $C$ of $G$. In this paper we characterize solvable groups $G$ in which the derived covering number is finite.
متن کاملGeneralization of Titchmarsh's Theorem for the Dunkl Transform
Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.
متن کامل